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The dual space of precompact groups

M. Ferrer, S. Hernández, V. Uspenskij (2013)

Commentationes Mathematicae Universitatis Carolinae

For any topological group G the dual object G ^ is defined as the set of equivalence classes of irreducible unitary representations of G equipped with the Fell topology. If G is compact, G ^ is discrete. In an earlier paper we proved that G ^ is discrete for every metrizable precompact group, i.e. a dense subgroup of a compact metrizable group. We generalize this result to the case when G is an almost metrizable precompact group.

The Minlos lemma for positive-definite functions on additive subgroups of n

W. Banaszczyk (1997)

Studia Mathematica

Let H be a real Hilbert space. It is well known that a positive-definite function φ on H is the Fourier transform of a Radon measure on the dual space if (and only if) φ is continuous in the Sazonov topology (resp. the Gross topology) on H. Let G be an additive subgroup of H and let G p c (resp. G b ) be the character group endowed with the topology of uniform convergence on precompact (resp. bounded) subsets of G. It is proved that if a positive-definite function φ on G is continuous in the Gross topology,...

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